Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,24,29)(20,30,32,42)(21,34,36,43)(22,28,23,27)(25,37,40,33)(26,38,41,35)(31,39,45,49)(44,46,48,47);(14,15)(16,17)(18,20)(19,25)(21,31)(22,37)(23,33)(24,32)(26,39)(27,42)(28,30)(29,40)(34,48)(35,47)(36,45)(38,46)(41,49)(43,44);(15,17)(18,21)(19,26)(20,31)(22,35)(23,38)(24,36)(25,39)(27,34)(28,43)(29,41)(30,44)(32,45)(33,46)(37,47)(40,49)(42,48);(20,32)(25,40)(30,42)(31,45)(33,37)(39,49)(44,48)(46,47)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16396);